scholarly journals ON A FUNCTIONAL CENTRAL LIMIT THEOREM FOR THE LINEAR PROCESS GENERATED BY ASSOCIATED RANDOM VARIABLES IN A HILBERT SPACE

2008 ◽  
Vol 23 (1) ◽  
pp. 133-140 ◽  
Author(s):  
Mi-Hwa Ko ◽  
Tae-Sung Kim
Keyword(s):  
Hilbert Space ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Linear Process ◽  
Functional Central Limit Theorem ◽  
Associated Random Variables ◽  
Functional Central Limit

scholarly journals Convergence of Weighted Linear Process forρ-Mixing Random Variables

2007 ◽  
Vol 2007 ◽  
pp. 1-7
Author(s):  
Guang-Hui Cai
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Linear Process ◽  
Functional Central Limit Theorem ◽  
Mixing Sequences ◽  
Functional Central Limit ◽  
Mixing Random Variables

A central limit theorem and a functional central limit theorem are obtained for weighted linear process ofρ-mixing sequences for theXt=∑i=0∞aiYt−i, where{Yi,0≤i<∞}is a sequence ofρ-mixing random variables withEYi=0,0<EYi2<∞,∑i=1∞ρ(2i)<∞. The results obtained generalize the results of Liang et al. (2004) toρ-mixing sequences.

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